Ms Croxall was presenting The Papers on Sunday evening when she seemingly laughed at a joke aimed at former Prime Minister Boris Johnson after he pulled out of the Tory leadership race.
The PA news agency understands she has now been ‘taken off air’ following the potential breach.
During her introduction to the programme, which started at 10.30pm on Sunday around 90 minutes after Boris Johnson pulled out of the Tory leadership race, Croxall said: “Well this is all very exciting isn’t it?” adding: “Am I allowed to be this gleeful? Well I am.”
In her first question to her guests she also remarked: “Can we even show you the front pages just yet, have they arrived? No they haven’t arrived. It’s all a little bit, you know, lastminute.com isn’t it? Because all the front pages were probably out of date by the time we received them.”
Some viewers, including several Tory MPs reacting to a clip on social media, complained it displayed bias.
BBC issues statement after Martine Croxall’s ‘potential breach of impartiality’
A statement from the broadcaster said: “BBC News is urgently reviewing last night’s edition of The Papers on the News Channel for a potential breach of impartiality.
“It is imperative that we maintain the highest editorial standards. We have processes in place to uphold our standards, and these processes have been activated.”